In mathematics, one often makes the remark that what is being talked about is a perfect idealized object. "Our planet is a sphere, but it's not really a perfect mathematical sphere (that is perfectly smooth, etc)."
What would one say, then, about natural numbers? In what way are they perfect?
My understanding is that there might be, e.g., two somethings in front of you, but these two somethings are never really the same somethings (e.g., because they are in two different places in space at the same time, so they are not really the same object). And because arguably, the number 2 does not exist inside of space and time, 2 represents "perfect twoness", so to speak.
Is my understanding correct? If not, what would a correct answer be?
In what sense are natural numbers perfect for the mathematical platonist?